Approximation numbers of weighted composition operators
We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators wit...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/69957 |
| Online Access: | https://hdl.handle.net/11441/69957 https://doi.org/10.1016/j.jfa.2018.01.010 |
| Access Level: | Open access |
| Keyword: | Composition operators Approximation numbers von Neumann algebras |
| Summary: | We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples). |
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